$\beta$-function of the level-zero Gross-Neveu model

Abstract

We explain that the supersymmetric $C{P}^{n-1}$ sigma model is directly related to the level-zero chiral Gross-Neveu (cGN) model. In particular, beta functions of the two theories should coincide. This is consistent with the one-loop-exactness of the $C{P}^{n-1}$ beta function and a conjectured all-loop beta function of cGN models. We perform an explicit four-loop calculation on the cGN side and discuss the renormalization scheme dependence that arises.

arXiv comment36 pages, 8 figures

References in corpus (27)

• Phases of $N=2$ Theories In Two Dimensions
• Supersymmetric vacua and Bethe ansatz
• Summing the Instantons: Quantum Cohomology and Mirror Symmetry in Toric Varieties
• Scheme dependence and the NSVZ $\beta$-function
• $N=1$ supersymmetry and the three loop gauge beta function
• Lectures on curved beta-gamma systems, pure spinors, and anomalies
• NSVZ scheme with the higher derivative regularization for N=1 SQED
• Four loop renormalization of the Gross-Neveu model
• The NSVZ beta-function in supersymmetric theories with different regularizations and renormalization prescriptions
• Scheme independent consequence of the NSVZ relation for N=1 SQED with N_f flavors
• On the Beta Function for Anisotropic Current Interactions in 2D
• Integrable 2d sigma models: quantum corrections to geometry from RG flow
• Three-loop Three-Linear Vertices and Four-Loop MOM beta functions in massless QCD
• The 4-loop beta-function in the 2D Non-Abelian Thirring model, and comparison with its conjectured "exact" form
• Principal Chiral Model on Superspheres
• Four loop MSbar mass anomalous dimension in the Gross-Neveu model
• Flag manifold sigma models: spin chains and integrable theories
• N=(0,2) Deformation of CP(1) Model: Two-dimensional Analog of N=1 Yang-Mills Theory in Four Dimensions
• Three loop renormalization of the SU(N_c) non-abelian Thirring model
• N=(0, 2) Deformation of (2, 2) Sigma Models: Geometric Structure, Holomorphic Anomaly and Exact Beta Functions
• Sigma models as Gross-Neveu models
• Quantum flag manifold $\sigma$-models and Hermitian Ricci flow
• The three-loop anomalous dimension and the four-loop $\beta$-function for $\mathcal{N}=1$ SQED regularized by higher derivatives
• The $\mathsf{C}{\mathsf{P}}^{\mathsf{n}-1}$-model with fermions: a new look
• Supersymmetric Tools in Yang-Mills Theories at Strong Coupling: the Beginning of a Long Journey
• Comments on the NSVZ $\beta$ Functions in Two-dimensional $\mathcal{N}=(0,2)$ Supersymmetric Models
• Integrable sigma models on Riemann surfaces